Provable Tempered Overfitting of Minimal Nets and Typical Nets

Itamar Harel, William M. Hoza, Gal Vardi, Itay Evron, Nathan Srebro, Daniel Soudry

Keywords: Deep Learning, Tempered Overfitting, Generalization

TL;DR: We prove that fully connected neural networks with quantized weights exhibit tempered overfitting when using both the smallest interpolating NN and a random interpolating NN.

Abstract: We study the overfitting behavior of fully connected deep Neural Networks (NNs) with binary weights that perfectly classify a noisy training set. We consider interpolation using both the smallest NN (having a minimal number of weights) and a random interpolating NN. For both learning rules, we prove overfitting is tempered. Our analysis rests on a new bound on the size of a threshold circuit consistent with a partial function. To the best of our knowledge, ours are the first theoretical results on benign or tempered overfitting that apply to deep neural networks and do not require an extremely high or low input dimension.

Student Paper: Yes

Submission Number: 22